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Math question - loan amortization

Math question - loan amortization

Old Aug 18th 2012, 3:48 am
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Default Math question - loan amortization

Hi,
This is really messing me up so sorry if it's a naive question. Here is the scenario.

Option 1. Buy a home for 550K, with 110k down and loan of 440K. 3 months into the loan make a one time payment 30K into the loan.
Option 2. Buy a home for 550K, with 140k down and loan of 410K

Both of them with 30 year fixed. Option 1 will be 3.825%. Option will be 3.7%.

As you can see around 3rd month into any of those two loan options I will roughly be 410k loan and Option 1 will be at higher interest rate. My thinking before I check out a financial calcultor would be Option 1 looks worse off because of higher interest rate.

However, I go here. http://www.excely.com/template/loan-calculator.shtml

Option 1 I end up up paying $242.9K interest and loan paid off in 318 months
Option 2 I end up paying $269.4K interest and loan paid off in 360 months

So I come out better under Option 1 (which at month 3 has same dollar amount debt but higher interest rate).

What am I missing here? Any math geeks or otherwise who can for sure tell me if I have got this right?
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Old Aug 18th 2012, 5:46 am
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Default Re: Math question - loan amortization

I haven't checked your calculations but surely the point is that with the second option, by making that extra $30,000 principal payment very early in the life of the loan you are reducing the term of the loan significantly - by 3 1/2 years according to your figures - which is why it ends up costing you less overall.

In other words the fact that the first option effectively becomes a 26 1/2 year loan instead of a 30 year loan is more significant than the difference of 0.125% in the interest rate.

The moral of this is that the last 0.1% on the interest rate really doesn't make nearly as much difference as how quickly you pay the loan off.

Last edited by md95065; Aug 18th 2012 at 5:57 am.
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Old Aug 18th 2012, 5:53 am
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Default Re: Math question - loan amortization

Originally Posted by md95065 View Post
I haven't checked your calculations but surely the point is that with the second option, by making that extra $30,000 principal payment very early in the life of the loan you are reducing the term of the loan significantly - by 3 1/2 years according to your figures - which is why it ends up costing you less overall.

In other words the fact that the second option is effectively a 26 1/2 year loan instead of a 30 year loan is more significant than the difference of 0.125% in the interest rate.

The moral of this is that the last 0.1% on the interest rate really doesn't make nearly as much difference as how quickly you pay the loan off.
Ditto. Your first loan has higher monthly payments since it is a larger loan so it is paid off earlier even though you paid off $30K early. The payments still remain the same which is higher than the second smaller loan.

Initially almost all of your payment is interest so paying off $30K early will probably reduce your interest portion of your payment by nearly $100 per month saving you over $20K over 26 years.

Last edited by Michael; Aug 18th 2012 at 6:00 am.
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Old Aug 18th 2012, 6:00 am
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Default Re: Math question - loan amortization

In other words the fact that the second option is effectively a 26 1/2 year loan instead of a 30 year loan is more significant than the difference of 0.125% in the interest rate.

Oops - I meant to say that the first option effectively becomes a 26 1/2 year loan - I have edited the original post to fix it there ...
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Old Aug 18th 2012, 1:58 pm
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Default Re: Math question - loan amortization

Thx very much. Kind favor. Could you, when you have 5 mins, put that into the calculator and see if you get the same result? And if you can validate its accuracy.

I understand it in theory. But just want someone else to check. Thanks in advance.
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Old Aug 18th 2012, 4:52 pm
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Default Re: Math question - loan amortization

Make sure that the mortgage does not have a prepayment penality. At one time, many mortgages had a prepayment penality if paid off before 3-5 years but no penalty was accessed if the home was sold before that time limit but I believe that has changed for most mortgages where there is no longer prepayment penalties. Even then, the prepayment penalty only occurred if more than a certain percentage of the mortgage was paid of early.
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Old Aug 19th 2012, 4:39 pm
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Default Re: Math question - loan amortization

Originally Posted by E3only View Post
Thx very much. Kind favor. Could you, when you have 5 mins, put that into the calculator and see if you get the same result? And if you can validate its accuracy.

I understand it in theory. But just want someone else to check. Thanks in advance.
Think of it this way. take two loans, one for 30k, and one for 410k. You pay for the total of 440k for three months and only 410k after. You saved the interest on the 30k. But you did even better because you kept on with the same monthly amount, paying off the 410k, early.
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Old Aug 19th 2012, 4:51 pm
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Default Re: Math question - loan amortization

Make sure that the mortgage does not have a prepayment penality.
x2. Although generally rare, its still not unheard of these days. Extra payments applied to the principal can count as a prepayment; general payoffs and refi's too. Check for riders/attachments to the original note etc. There are not set rules about when and how much they'll charge but most banks don't do ppp because of the bad rap they got a few years ago, but they still do exist. Have you considered 15yr or 20 yr loans (with or w/o the extra payments), or is it the monthly you're conscious of?
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Old Aug 19th 2012, 11:03 pm
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Default Re: Math question - loan amortization

Originally Posted by paddingtongreen View Post
Think of it this way. take two loans, one for 30k, and one for 410k. You pay for the total of 440k for three months and only 410k after. You saved the interest on the 30k. But you did even better because you kept on with the same monthly amount, paying off the 410k, early.
Yes, I am finally getting around that concept! Thx a lot.
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Old Aug 19th 2012, 11:06 pm
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Default Re: Math question - loan amortization

Originally Posted by Tarkak9 View Post
x2. Although generally rare, its still not unheard of these days. Extra payments applied to the principal can count as a prepayment; general payoffs and refi's too. Check for riders/attachments to the original note etc. There are not set rules about when and how much they'll charge but most banks don't do ppp because of the bad rap they got a few years ago, but they still do exist. Have you considered 15yr or 20 yr loans (with or w/o the extra payments), or is it the monthly you're conscious of?
Well, in Australia where most of the loans are variable, you are free to pay as much excess as you can and you can draw it back from the account without disturbing the interest rate.

For me, it does not matter if its 30 year of 20 because any extra money I have I will put it into mortgage anyway. The tricky bit is, I have not heard of a bank that offers the draw back of funds. So my thought was might as well keep the EMI low and pay extra as I go. I then have to bear in mind that I can not draw back so almost have to keep saving and then over and above the savings, I can pay mortgage over and above the EMI if that makes sense......
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Old Aug 20th 2012, 3:35 am
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Default Re: Math question - loan amortization

Originally Posted by E3only View Post
Well, in Australia where most of the loans are variable, you are free to pay as much excess as you can and you can draw it back from the account without disturbing the interest rate.

For me, it does not matter if its 30 year of 20 because any extra money I have I will put it into mortgage anyway. The tricky bit is, I have not heard of a bank that offers the draw back of funds. So my thought was might as well keep the EMI low and pay extra as I go. I then have to bear in mind that I can not draw back so almost have to keep saving and then over and above the savings, I can pay mortgage over and above the EMI if that makes sense......
The only type of loans that allow you to draw back funds are HELOCs (Home Equity Lines of Credit). Generally those are only given when you build up enough equity in a home and need money for just about anything. Normally you get a line of credit (eg. $100,000) and you can draw on that money as needed for a small fee of about $50 per year plus interest on any money drawn. You may possibly never draw money or you could possibly draw the full amount at one time and there isn't any fixed payment amount but you must pay the interest each month on the money drawn and pay off the loan by the time the term of the HELOC expires (usually 15 years).
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Old Aug 20th 2012, 2:09 pm
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Default Re: Math question - loan amortization

Originally Posted by Michael View Post
The only type of loans that allow you to draw back funds are HELOCs (Home Equity Lines of Credit). Generally those are only given when you build up enough equity in a home and need money for just about anything. Normally you get a line of credit (eg. $100,000) and you can draw on that money as needed for a small fee of about $50 per year plus interest on any money drawn. You may possibly never draw money or you could possibly draw the full amount at one time and there isn't any fixed payment amount but you must pay the interest each month on the money drawn and pay off the loan by the time the term of the HELOC expires (usually 15 years).
Thanks though that HELOC will have higher interest rates ? I mean say in 3 years I apply. At that time 30 year fixed is 4.5%. I assume HELOC will be higher than 4.5%?
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Old Aug 20th 2012, 2:27 pm
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Default Re: Math question - loan amortization

Originally Posted by E3only View Post
Thanks though that HELOC will have higher interest rates ? I mean say in 3 years I apply. At that time 30 year fixed is 4.5%. I assume HELOC will be higher than 4.5%?
HELOCs are always variable interest rates loans usually a certain percentage above some regional money index so the interest rate could be a lower or higher but definitely more risky than a fixed rate loan if interest rates rise. Like any variable rate loan, you could refinance to a fixed rate loan to lock in a fixed rate but by that time it is usually too late since the fixed rate interest rate will be high.

Also HELOCs don't offer the protection of other mortgages (especially original purchase 1st and 2nd loans) if a foreclosure should occur. In many states, the bank can't demand payment on shortfalls if a foreclosure or bankruptcy would occur on certain types of loans (non recourse loans).

The following defines the difference between recourse and non recourse loans and the states that have non recourse loans. Even states that have recourse laws seldom come after the shortfall since they can't get blood from a turnip but HELOCs are especially vulnerable since they are just a line of credit and don't follow standard mortgage laws but laws more like a credit card where a bank can get a judgement and then extend that judgement for years by getting a garnishment order.

http://banking.about.com/od/loans/a/recourseloan.htm

http://www.cardreport.com/laws/statu...mitations.html

http://www.bcsalliance.com/y_debt_st...nishments.html

So even in non recourse states, foreclosures are expensive and getting a judgment has limited time frames and added costs so unless a person is sitting on a bundle of money, banks seldom get a judgment. On the other hand, states like California allow a person to walk away from non recourse loans just because the property is underwater even though the person may have millions in the bank. In fact some in California have purchased a second home as their primary residence and paid a low down payment and got a good interest rate while their credit was good and then immediately quit making payments on their other home that was underwater causing it to go into foreclosure. So their credit score was good when they purchased the second home and tanked when the foreclosure occurred but they then didn't need any more money and rebuilt their credit score for the future.

Last edited by Michael; Aug 20th 2012 at 3:11 pm.
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Old Aug 20th 2012, 4:04 pm
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Default Re: Math question - loan amortization

Thanks very much. I am going to stay away from the HELOCs for sure......
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Old Aug 20th 2012, 4:12 pm
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Default Re: Math question - loan amortization

Originally Posted by E3only View Post
Thanks very much. I am going to stay away from the HELOCs for sure......
I would HELOCS are what most of S. CA live on which is why they always have shiny new cars and bright holidays. Its the 'keep up with the Jones' loan. And then.... when everything crashes its why they whine that they don't have any equity.

Of course, carefully planned that could be a good thing - but I think they call that fraud
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